Beryllium monohydride (BeH): Where we are now, after 86 years of spectroscopy Nikesh S. Dattani ⇑ Physical and Theoretical Chemistry Laboratory, Department of Chemistry, Oxford University, OX1 3QZ Oxford, UK Quantum Chemistry Laboratory, Department of Chemistry, Kyoto University, 606-8502 Kyoto, Japan article info Article history: Received 10 August 2014 In revised form 18 September 2014 Available online 17 October 2014 Keywords: Ultra-high precision Interstellar chemistry & astrochemistry Fundamental molecules Early universe chemistry Big Bang physics Potentiology & potential energy curves and surfaces Halo nucleonic molecules Theory vs experiment Exoplanet atmosphere Cool stars Stellar chemistry and the Sun Isotope effect Dispersion constants abstract BeH is one of the most important benchmark systems for ab initio methods and for studying Born–Oppen- heimer breakdown. However the best empirical potential and best ab initio potential for the ground electronic state to date give drastically different predictions in the long-range region between where the highest measurements have been made, and the dissociation energy; a region which is about 1000 cm 1 for 9 BeH,  3000 cm 1 for 9 BeD, and 13 000 cm 1 for 9 BeT. Improved empirical potentials and Born–Oppenheimer breakdown corrections have now been built in this work for the ground elec- tronic states Xð1 2 R þ Þ of all three isotopologues. The predicted dissociation energy for 9 BeH from the new empirical potential is now in agreement with the current best ab initio prediction in all 5 digits of the former’s precision, while the previous best empirical potential was in disagreement by 74 cm 1 . The previous best empirical potential predicted the existence of unobserved vibrational levels for all three isotopologues, and the current best ab initio study also predicted the existence of all of these levels, and 7 more in total. With the exception of two, the present empirical potential agrees with the existence of all of the ab initio potentials’ extra levels not predicted by the earlier empirical potential. With one exception, all energy spacings between vibrational energy levels for which measurements have been made, are predicted with an agreement of better than 1 cm 1 between the new empirical potential and the current best ab initio potential, but some predictions for unobserved levels are still in great disagreement, and the equilibrium bond lengths are different by orders of magnitude. Ó 2014 Elsevier Inc. All rights reserved. 1. Introduction With only 5e  , BeH is the simplest neutral open shell molecule, and is therefore of paramount importance in benchmarking ab ini- tio methods. The first Hartree–Fock level endeavor was in 1967 [1], and it has remained the subject of a plethora of theoretical studies since then [2–79]. It is also the second lightest neutral heteronu- clear molecule after LiH, and one of the only neutral diatomics for which spectroscopic measurements on a tritium isotopologue have been performed, making it a very important benchmark system for studying the breakdown of the Born–Oppenheimer approximation [51,74,78,80–82]. Due to its simplicity, BeH is expected to be present in astronomical contexts such as exoplane- tary atmospheres, cool stars, and the interstellar medium [83], but in the context of astronomy, has only been found on our Sun (see [84,85]). Finally, the extraordinarily long half-life of the halo nucleonic atom 11 Be makes 11 BeH a compelling candidate for the formation of the first halo nucleonic molecule [81]. Spectroscopic measurements on 9 BeH date back to 1928 [86,87], and on 9 BeD date back to 1935 [88]. By 1937 there was already an octad of publications on the molecule [86–93]. Since then, higher-resolution spectra have been measured for both of these isotopologues, and also for 9 BeT in [10]. Various types of experiments on BeH have been performed over the years, including those described in [10,18,80,94–102]. Before the present paper, the most thorough empirical analysis of 9 BeH, 9 BeD, and 9 BeT was that of [80], where empirical potentials were built for all three isotopo- logues, based on a fit to data from [10,18,80,99,102]. This state of the art 2006 empirical study left behind various mysteries which remained unsolved for the last 8 years: 1. The 2006 study predicted that the 9 BeH dissociation energy was D e ¼ 17 590  200 cm 1 [80] which is higher than the value of D e ¼ 17 426  100 cm 1 in the 1975 experimental study [95] by more than the latter’s uncertainty. The most recent ab initio study (published in 2011) of 9 BeH [78] http://dx.doi.org/10.1016/j.jms.2014.09.005 0022-2852/Ó 2014 Elsevier Inc. All rights reserved. ⇑ Address: Physical and Theoretical Chemistry Laboratory, Department of Chem- istry, Oxford University, OX1 3QZ Oxford, UK. E-mail address: dattani.nike@gmail.com Journal of Molecular Spectroscopy 311 (2015) 76–83 Contents lists available at ScienceDirect Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms